There are 3 advantages to the Clicky.
1. User replaceable rubber switch button.
2. Grit can't get under the start of the switch cap. I don't mean into the switch cap, but on the Rotary there is a little section grit could get under before it reaches one of the two O-rings keeping it out. This would give it a gritty feel until washed out, but wouldn't effect performance as it can't get into the workings of the tail.
3. When used under water, if one Rotates the Rotary dial, there is more likelihood of water getting in there as they are static seals... probably not a huge deal, but still, there it is.
I'll add:
4. User replaceable o-ring in the tailcap. Also possible to do maintenance, such as apply grease to o-ring many years later, or check for wear and tear.
5. No moving parts (besides the electronic switch), so it will no doubt last longer. Important in a SHFT, doomsday scenario.
6. Predictability of brightness. You always know what brightness your light will come on at. i.e. with the Executive "It turns on to Medium (level 16) - ensuring enough light for most common tasks and long run times", and with the LE, and it's design purpose, it is arguably essential that it comes on in high every time: "The EDC LE turns on to High so you always have enough light for potentially tactical situations."
7. Predictability of runtimes. Each level of the Clicky has a documented minimum runtime. This is important when estimating battery usage and how many spares to carry.
8. Rock solid tailcap, no wobbly play in the threads. Great for OCD types.
9. A long history. The EDC Executive has pretty much the same physical appearance and interface as the original EDC Basic 42 / EDC Extreme 42. While EDC LE is essentially just an upgraded maximum brightness of the Basic 60 LE.
10. Slightly cheaper.
11. Easier production process (I recall that the Clicky models were still being produced and sold even when HDS had production issues with the Rotary models, circa 2015(?)).
12. It has a proper clip available (for those that want one). The clip wasn't an after thought and doesn't become loose and fall off like the Universal pocket clip available for the Rotary.